Weak itinerant ferromagnetism and electronic and crystal structures of alkali-metal iron antimonides: NaFe4Sb12 and KFe 4Sb12

Article abstract of DOI:10.1103/PhysRevB.70.214418

The synthesis, chemical, structural, and magnetic properties of alkali-metal compounds with filled-skutterudite structure, NaFe ₄Sb₁₂ and KFe₄Sb₁₂, are described. X-ray and neutron diffraction and elemental analysis established the crystal structure without defects and disorder on the cation site. The temperature and pressure dependence of the cubic unit cell of NaFe₄Sb₁₂ and the displacement parameter of Na are investigated. The electronic structure is calculated by density functional methods (LMTO, FPLO). Quantum chemical calculations (electron localization function) reveal the covalent character of both Fe-Sb and Sb-Sb interactions. Electronic structure calculations within the local density approximation exhibit a band ferromagnetic ground state and predict a half-metallic behavior. In contrast to isostructural alkaline-earth compounds (CaFe₄Sb₁₂ and BaFe₄Sb₁₂), the alkali-metal skutterudites are itinerant electron ferromagnets with small magnetic moments (≈0.25 μ_B/Fe atom) and T_C≈=85 K. Yet the paramagnetic moments of all four compounds are between 1.5 μ_B and 1.7 μ_B per Fe atom, indicating similar Stoner factors. Temperature-dependent ⁵⁷Fe and ¹²¹Sb Moessbauer spectroscopies confirm the ferromagnetic state in the sodium compound with very small hyperfine fields at the iron and antimony sites.

Full text of DOI:10.1103/PhysRevB.70.214418

PHYSICAL REVIEW B 70, 214418 (2004)
Weak itinerant ferromagnetism and electronic and crystal structures of alkali-metal iron
antimonides: NaFe4Sb12 and KFe4Sb12
A. Leithe-Jasper, W. Schnelle, H. Rosner, M. Baenitz, A. Rabis, A. A. Gippius,† E. N. Morozova,† H. Borrmann,
*
U. Burkhardt, R. Ramlau, U. Schwarz, J. A. Mydosh,‡ and Y. Grin
Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany
V. Ksenofontov and S. Reiman
Institut für Anorganische Chemie und Analytische Chemie, Johannes-Gutenberg-Universität Mainz, Staudinger-Weg 9,
55099 Mainz, Germany
(Received 14 May 2004; revised manuscript received 13 August 2004; published 17 December 2004)
The synthesis, chemical, structural, and magnetic properties of alkali-metal compounds with filled-
skutterudite structure, NaFe4Sb12 and KFe4Sb12, are described. X-ray and neutron diffraction and elemental
analysis established the crystal structure without defects and disorder on the cation site. The temperature and
pressure dependence of the cubic unit cell of NaFe4Sb12 and the displacement parameter of Na are investigated.
The electronic structure is calculated by density functional methods (LMTO, FPLO). Quantum chemical
calculations (electron localization function) reveal the covalent character of both Fe-Sb and Sb-Sb interac-
tions. Electronic structure calculations within the local density approximation exhibit a band ferromagnetic
ground state and predict a half-metallic behavior. In contrast to isostructural alkaline-earth compounds
(CaFe4Sb12 and BaFe4Sb12), the alkali-metal skutterudites are itinerant electron ferromagnets with small mag-
netic moments (Ϸ0.25␮B/Fe atom) and TCϷ85 K. Yet the paramagnetic moments of all four compounds are
between 1.5␮ and 1.7␮ per Fe atom, indicating similar Stoner factors. Temperature-dependent 57Fe and
B
B
121Sb Mössbauer spectroscopies confirm the ferromagnetic state in the sodium compound with very small
hyperfine fields at the iron and antimony sites.
DOI: 10.1103/PhysRevB.70.214418
PACS number(s): 75.50.Bb, 75.40.Cx, 71.20.Lp, 76.80.ϩy
I. INTRODUCTION
and 8. All these studies suggest that the physics of filled
skutterudites is governed by a subtle interplay of the filler
ions and their surrounding transition-metal pnicogen host
structure.
In order to gain a better understanding of these processes
and to explore non-rare-earth skutterudites, we have success-
fully synthesized new alkali-metal compounds with sodium
and potassium.9 The filler atoms are s-electron metals of
small mass that are not magnetic and, therefore, are a good
choice for the investigation of the d-electron influence on the
properties of filled skutterudites.
In this article, we present our investigations of the re-
cently synthesized skutterudites NaFe4Sb12 and KFe4Sb12.
These materials exhibit bulk ferromagnetic transitions at TC
Ϸ85 K with weak itinerant iron magnetic moments and
strong spin fluctuations.9 We propose that these compounds
belong to the class of half-metallic ferromagnets,10 which are
promising materials for spin-electronic devices (spintronics).
We compare them with the alkaline-earth (Ca, Ba) com-
pounds previously studied by Danebrock, Evers, and
Jeitschko11 which remain paramagnetic down to helium tem-
peratures.
The class of compounds known as “skutterudites” exhib-
its a wealth of topical behaviors, which are the source and
motivation of increasing interest and efforts to study and
understand the underlying physics. All these materials derive
from the archetypal mineral skutterudite ͑CoAs3͒.1 Binary
skutterudites having the general chemical formula TX3 are
formed by the members of the ninth group of the periodic
system T=͑Co,Rh,Ir͒ with pnicogens X=͑P,As,Sb͒. No bi-
nary compounds with iron, ruthenium, and osmium could be
synthesized under equilibrium conditions. In order to stabi-
lize such compounds it is necessary to include electroposi-
tive elements as a third component leading to the total for-
mula RyT4X12 (filled skutterudites2). Here, R can be an
alkaline-earth, rare-earth, and actinide metal or thallium. Dif-
ferent degrees of filling y can be realized up to y=1; how-
ever, the real limits for y depend strongly on the “filler” R
and the “host” T4X12 and are not yet well explored. These
compounds RyT4X12 are called “filled” since the stabilizing
atoms reside in large voids already present in the transition-
metal pnicogen framework (see Ref. 2 and Fig. 3).
A variety of properties has been observed for rare-earth-
filled skutterudites ranging from metal-insulator transitions
to magnetic and quadrupole orderings, conventional and un-
conventional superconductivity, heavy fermion and non-
Fermi liquids, and fluctuating and mixed valency.3–6 Further-
more, interest in these compounds is fueled by their possible
use in thermoelectric applications.7,8 For exhaustive reviews
on the skutterudite physics and chemistry we refer to Refs. 3
Section II will describe our experimental techniques, re-
garding synthesis, structural, and physical properties and the
calculational methods of electron localization function (ELF)
and band structure. In Sec. III we show results for the crystal
structure, chemical bonding, and electronic band structure
along with the magnetic properties of the two ferromagnetic
compounds (Na and KFe4Sb12) and the isostructural Ca and
Ba skutterudites. 57Fe and 121Sb Mössbauer spectroscopy for
1098-0121/2004/70(21)/214418(12)/$22.50
214418-1
©2004 The American Physical Society

LEITHE-JASPER et al.
PHYSICAL REVIEW B 70, 214418 (2004)
NaFe4Sb12 is employed to determine the hyperfine splitting
in the ferromagnetic ground state of the sodium compound.
Finally, Sec. IV summarizes the results.
Guinier Huber technique using LaB6 as an internal standard
͑a=4.156 92 Å͒. Low-temperature powder XRD was per-
formed on a Huber Guinier camera with a sample holder
incorporated in a closed-cycle helium cryostat. For correct
lattice parameter determination, the measurement was per-
formed with silicon powder ͑a=5.431 194 6 Å͒ used as an
internal standard.13 Powder neutron diffraction data were
collected at the Hahn-Meitner-Institut, Berlin, with instru-
ment E9. Single-crystal data were collected on a Stoe IPDS
system (Ag K␣ radiation; ␭=0.560 86 Å) and on an Rigaku
R-axis RAPID diffractometer (Mo K␣ radiation 0.710 73 Å).
Crystallographic calculations were made with the WINCSD
(Ref. 14) and the SHELXL-97 (Ref. 15) program packages.
II. EXPERIMENT
A. Synthesis
Due to the high vapor pressure of the alkali metals, poly-
crystalline samples of NaFe4Sb12 and KFe4Sb12 were pre-
pared in a two-step synthesis. First, the binary compounds
NaSb and KSb were synthesized from the elements (Na, K,
99.99% from ABCR; Sb, shot, 99.99% ChemPur) in a sealed
tantalum ampoule. Then, a stoichiometric mixture of pow-
dered alkali-metal monoantimonides together with FeSb2
(Fe, powder, 99.9% ChemPur) and elemental Sb was com-
pacted to a pellet which was annealed in a sealed Ta ampoule
at 400 °C for 1 week, followed by regrinding and additional
heat treatment cycles. Since binary alkali-metal antimony
compounds are very sensitive to air, all these steps were
carried out in an argon-filled glove box with oxygen and
moisture content less 1 ppm.
The ternary compounds were obtained as dark gray pow-
ders. In contrast to the educts, they are not at all sensitive to
air or moisture. The compounds CaFe4Sb12 and BaFe4Sb12
were synthesized in a similar manner. Compacted blends of
FeSb2, Sb, CaSb2, and BaSb2, respectively, were annealed at
500 °C in sealed Ta tubes.
Single-crystal grains of NaFe4Sb12 could be isolated from
a sample which was heated to 700 °C and furnace cooled in
order to obtain larger grains. Physical properties measure-
ments were performed on specimens cut from compacted
samples which were prepared by spark plasma sintering12
(SPS) the powders at 200 °C and at a pressure of 600 MPa
for 3 h under an atmosphere of argon. In this way, 92% of
the theoretical density of the bulk material could be
achieved.
Metallographic microstructure analyses on polished sur-
faces were performed with optical microscopy and electron-
probe microanalysis (EPMA). The latter investigations were
done with a wavelength-dispersive (WDX) Cameca SX100
system. Elemental standards for iron and antimony and NaCl
as a sodium standard were used. Energy-dispersive analysis
(EDX) of the samples was carried out in a Philips XL30
scanning electron microscope. These investigations revealed
elementary antimony as a common impurity phase (about
2 vol. %) present after SPS treatment.
C. Physical properties
Magnetic properties were measured on a superconducting
quantum interference device (SQUID) magnetometer
(MPMS XL-7, Quantum Design). Zero-field cooling (ZFC,
measured in warming) and field-cooling (FC) runs and iso-
thermal magnetization loops were performed up to Hext
=70 kOe. Additional isothermal magnetization curves up to
H
ext=140 kOe were measured by an extraction technique
(PPMS, Quantum Design). No demagnetization or diamag-
netic core corrections were applied.
Mössbauer measurements of powder samples of
NaFe4Sb12 were performed in a transmission geometry using
a constant-acceleration spectrometer and a helium bath cry-
ostat. 57Fe Mössbauer spectra were recorded at room tem-
perature and 4.2 K using the 50 mCi source 57Co͑Rh͒. The
RECOIL 1.03 Mössbauer analysis software was used to fit the
experimental spectra.16 Isomer shift values are quoted rela-
tive to ␣-Fe at 293 K. For Sb Mössbauer spectroscopy, a
121mSn͑CaSnO3͒ source with an activity of 3.0 mCi was
placed together with the absorber in the helium bath cryostat.
The spectra were analyzed with the program EFFI (Ref. 17)
using the transmission integral. During the fit the source
recoil-free fraction value was kept 0.6.
D. Calculation procedures
Linear muffin-tin orbital (LMTO) method. The tight-
binding (TB) LMTO atomic sphere approximation (ASA)
program package18 with exchange correlation potential [local
density approximation (LDA)] according to Barth and
Hedin19 was used for quantum chemical calculations on
NaFe4Sb12. The radial scalar-relativistic Dirac equation was
solved to obtain the partial waves. Although the calculation
within the ASA includes corrections for the neglect of inter-
stitial regions and partial waves of higher order,20 an addition
of empty spheres in the case of NaFe4Sb12 was not necessary.
The following radii of atomic spheres were used: r͑Na͒
=2.642 Å, r͑Fe͒=1.528 Å, and r͑Sb͒=1.714 Å. A basis set
containing Na͑3s͒, Fe͑4s,4p,3d͒, and Sb͑5s,5p͒ orbitals
was employed for the self-consistent calculations with the
Na͑3p,3d͒ and Sb͑5d,5f͒ functions being downfolded. The
calculation was performed spin-polarized.
Magnetization measurements (see below) showed that as-
synthesized powders and SPS-treated samples contained a
ferromagnetic impurity with a Curie temperature well above
400 K. This impurity is most probably metallic iron (TC
=1043 K). The content is some 100 ␮g/g, well below the
detection limits of conventional analytical methods. Batches
of skutterudite material were therefore finely powdered,
etched in hydrochloric acid (HCl; 20%), and rinsed in dis-
tilled water repeatedly. This treatment strongly reduced the
amount of ferromagnetic impurities.
B. Structure investigations
Electron localization function (ELF). The ELF was evalu-
Powder x-ray diffraction (XRD) measurements were
made using Cu K␣1 radiation ͑␭=1.540 60 Å͒ applying the
ated according to Savin et al.21,22 with an ELF module al-
214418-2

WEAK ITINERANT FERROMAGNETISM AND…
PHYSICAL REVIEW B 70, 214418 (2004)
¯
TABLE I. Crystallographic data of cubic NaFe4Sb12 at different temperatures. Structure type: LaFe4P12. Space group: Im3, Z=2. Na is
in 2a (0,0,0); Fe in 8c 41 , 41 , 41 . Sb in 24g (0, y, z).
͑
͒
Coordinates
Displacement parameters
Interatomic distances
iso
T
[K]
a
[Å]
U
d1,d2͑Sb-Sb͒
d͑Fe-Sb͒
[Å]
d͑Na-Sb͒
[Å]
Fe
iso
Na
iso
Sb
y
z
U
͓10−3 Å2͔
U
[Å]
295a
300b
50b
2b
9.1767(5)
9.1759(3)
9.1541(5)
9.1524(2)
0.1588(1)
0.1593(4)
0.1584(4)
0.1588(4)
0.3369(1)
0.3363(4)
0.3362(4)
0.3369(4)
22.0(3)
41(5)
13(3)
8(3)
3.5(3)
4.4(6)
5.2(4)
3.7(5)
5.3(4)
6.5(5)
4.3(6)
3.2(5)
2.99(1), 2.91(1)
3.00(1), 2.93(1)
3.00(1), 2.91(1)
2.99(1), 2.91(1)
2.57(1)
2.57(2)
2.56(1)
2.56(2)
3.417(1)
3.415(4)
3.406(4)
3.409(4)
aFrom room-temperature single-crystal XRD data: R=0.014, wR2=0.025.
bFrom powder neutron diffraction data: T=300 K: Ri=0.041, RP=0.12. T=50 K: Ri=0.042, RP=0.12. T=2 K: Ri=0.039, RP=0.11.
ready implemented within the TB-LMTO-ASA program
package.18 To gain a deeper insight in the chemical bonding,
the topology of the ELF was analyzed with the program
BASIN.23 The electron density was integrated in the basins
which are bounded by zero flux surfaces in the ELF gradient
field. This method, analogous to the procedure proposed by
Bader for the electron density,24 gave electron counts for
each basin, which reveal basic information for the descrip-
tion of the bonding situation.
Full-potential local-orbital (FPLO) scheme. To obtain
more accurate total energies and detailed electronic structure
information, in addition, a full-potential nonorthogonal local-
orbital calculation scheme25 within the L(S)DA was used. In
the scalar-relativistic calculations the exchange and correla-
tion potentials of Perdew and Wang26 were used. As the
basis set, Na͑2s,2p,3s,3p,3d͒, Fe͑3s,3p,4s,4p,3d͒, and
Sb͑4s,4p,4d,5s,5p,5d͒ states were employed. The lower-
lying states were treated fully relativistically as core states.
The Na 3d states as well as the Sb 5d states were taken into
account as polarization states to increase the completeness of
the basis set. The treatment of the Na͑2s,2p͒, Fe͑3s,3p͒, and
Sb͑4s,4p,4d͒ semicorelike states as valence states was nec-
essary to account for non-negligible core-core overlaps. The
spatial extension of the basis orbitals, controlled by a confin-
ing potential ͑r/r0͒4, was optimized to minimize the total
energy.27 A k mesh of 396 points in the irreducible part of the
Brillouin zone (8000 in the full zone) was used to ensure
accurate density of states and band structure information,
especially in the region close to the Fermi level.
cupancy. Iron and antimony positions also do not show any
deviation from full occupancy. This result is also confirmed
by WDX analysis of a polished surface of the sample from
which the single crystal for structure analysis was selected.
The composition Na0.95͑1͒Fe4.08͑1͒Sb11.29͑1͒ is obtained. Addi-
tionally, the WDX-EPMA of SPS-treated bulk samples gives
a
composition
of
Na0.97͑3͒Fe4.06͑2͒Sb11.95͑3͒
and
K0.98͑1͒Fe4.05͑2͒Sb11.97͑3͒, respectively.
At room temperature sodium shows a large displacement
parameter (see Table I). Since the chemical analysis of our
material gives no evidence of partial occupation, we can rule
out defects on this position on the level of 3%.
In order to obtain more information about the displace-
ment factors, the crystal structure of NaFe4Sb12 as a function
of temperature was investigated from powder neutron dif-
fraction data (see Table I). The atomic displacement param-
2
eter Uiso=Biso/8␲ of Na is strongly temperature dependent,
while the values for Sb and Fe show only a weak dependence
or almost no dependence on temperature, respectively. At
2 K the Uiso values for all three positions are of similar mag-
nitude close to zero (Fig. 1). The difference between the
displacement parameters for Na and Fe (Sb) extrapolated to
0 K is less than 0.005 Å2, which range roughly 3 mean e.s.d.
This reveals only the conventional dynamic thermal motion
(Einstein oscillator) of sodium atoms inside the slightly over-
sized antimony cage.
It has been speculated that the skutterudites are therefore
prone to various kinds of displacive-type phase
transitions28,30 where at lower temperatures the configuration
becomes increasingly unstable due to freezing of the thermal
motion of the filler atoms31 which might then lock-in to off-
center positions in the cages28,30 and, thus, possibly induce
structural distortions which could lower the crystal symme-
try. Indications of static off-center movement have been in-
deed found in metastable skutterudites filled with heavy rare
earths.32,33 However, no indications of a lock-in-type phase
transition were found for NaFe4Sb12. At room temperature,
off-center displacements of the sodium atom can be ruled out
due to the spherical distribution of the difference electron
density34 in the vicinity of the Na position (Fig. 2).
III. RESULTS AND DISCUSSION
A. Crystal structure
Powder XRD data give cubic lattice parameters a
=9.1767͑5͒ Å for NaFe4Sb12 and a=9.1994͑5͒ Å for
KFe4Sb12, respectively. These values are larger than those in
CaFe4Sb12 [a=9.1634͑4͒ Å; cf. a=9.162͑1͒ Å (Ref. 28)] but
smaller than for BaFe4Sb12 [a=9.2058͑2͒ Å; cf.
a
=9.202͑2͒ Å (Ref. 28); a=9.200͑3͒ Å (Ref. 29)]. Single-
crystal XRD analysis (see Table I) of NaFe4Sb12 corroborates
the full occupancy (100%) of the 2a site by sodium. The
refinement of the occupancy for the sodium position does not
improve the residual values in comparison with the full oc-
Thermal expansion of NaFe4Sb12 was studied by powder
XRD (determination of the cubic lattice parameter) in the
temperature range from 15 K to 300 K and is rather small.
For the temperature range 100–300 K (with an approxi-
214418-3

LEITHE-JASPER et al.
PHYSICAL REVIEW B 70, 214418 (2004)
FIG. 2. Experimental difference electron density distribution
around the Na position in NaFe4Sb12. “ϩ” indicates the position of
the sodium atom. Dashed lines shows the zero level; the isolines are
drawn with the step 5e−/Å3; the step width on each axis is 0.2 Å.
FIG. 1. Upper panel: temperature dependence of the cubic lat-
tice parameter (b) for NaFe4Sb12 from the powder x-ray diffraction
data. Isotropic displacement parameters Uiso for Na (squares), Fe
(circles), and Sb (triangles) are displayed. Lower panel: pressure
dependence of the unit cell volume. The line represents a fit of a
Murnaghan equation of state.
bility of a skutterudite structure to compression [B0
=136͑5͒ GPa, BЈ0 =4.8͑5͒] was found for the binary com-
pound IrSb3.40
mately linear slope of a) the coefficient of linear expansion
␣=11ϫ10−6 K−1 which is only slightly larger than 9
ϫ10−6 K−1 derived from neutron diffraction data for
LaFe4Sb12.31 According to these data, the iron-antimony
framework is rather rigid. Similar conclusions were drawn
from lattice dynamics calculations.35,36 Also the high Debye
temperature for the Os-Sb framework in PrOs4Sb12
[Ϸ375 K (Ref. 33)] and for CoSb3 [307 K (Ref. 37)] gener-
ally point to a rigid skutterudite lattice. No indications of
possible structural transitions are found from the temperature
dependence of the lattice parameters for NaFe4Sb12 (see Fig.
1 and the distances listed in Table I).
The pressure dependence of the unit cell volume of
NaFe4Sb12 (Fig. 1) in the range up to 9.5 GPa is character-
istic for intermetallic compounds. The least-squares fit of a
Murnaghan-type equation of state38 to the experimental data
leads to the zero-pressure unit cell volume V0=772.78 Å3
and a bulk modulus (at p=0) B0=85͑1͒ GPa using BЈ0 =4
(fixed first derivative). A similar value of B0=88͑4͒ GPa was
recently found for the intermetallic compound YbAgGa2
with a covalently bonded polyanion ͓AgGa2͔.39 A higher sta-
B. Chemical bonding and electronic structure
The electron localization function (ELF, ␩, normalized to
values between 0 and 1) is an appropriate tool for the inves-
tigation of chemical bonding in real space21,22 and helps in
understanding the nature of the atomic interactions. For more
details we refer to Refs. 41 and 42.
The positions of the ELF maxima (attractors) visualize the
direct interatomic bonds in the structure (real space). The
topological analysis of the ELF of NaFe4Sb12 displays only
three types of attractors in the valence region (see Fig. 3).
Two of them are located on the shortest Sb-Sb contacts d1
and d2 in the Fe-Sb framework (cf. Table I and Fig. 3),
confirming the covalent character of the interaction between
the antimony atoms belonging to the neighboring ͓FeSb6͔
octahedrons. The third one is located slightly shifted off the
Fe-Sb bond lines, showing a pronounced covalency of these
bonds [Fig. 3(b)]. No unique attractors were found in the
valence region in between the sodium and framework atoms
(antimony or iron).
214418-4

WEAK ITINERANT FERROMAGNETISM AND…
PHYSICAL REVIEW B 70, 214418 (2004)
Sb contacts the count of 2.03 electrons was observed ͓Fig.
3͑b͔͒. For the inner shell of the iron atoms, 13.76 elec-
trons were found ͑instead of the 14 expected͒, which is in
good agreement with the calculation for free atoms43 and
confirms the participation of the inner-shell electrons in
the interactions in the valence region. For the core region
of the sodium atoms 9.98 electrons were found from the
integration procedure in good agreement with ten ex-
pected from the Aufbau principle for Na+. This would give
a charge transfer of 1.02 electrons from each sodium to
the polyanion. On the other hand, the polyanion Fe4Sb12 is
formed by 6 Sb-Sb ͑d1͒, 6 Sb-Sb ͑d2͒, and 24 Fe-Sb
bonds. This gives a total count of 69.90 electrons for the
polyanion and suggests a charge transfer of 0.94 electrons
from each sodium to the polyanion ͑subtracting 12ϫ5e−
of Sb and 4ϫ2.24e− of Fe from 69.90e−͒. Both evaluation
procedures give similar results; thus, the mean value of
charge transfer is 0.98 electrons. Accordingly, the total
0.98−
electron balance can be written as Na0.98+͓Fe4Sb12͔
.
Considering the strong overlap of the 3s band of Na with
Sb 5p band in the density of states (DOS) (see below) and
taking into account the rectangular arrangement of the Sb-
Sb bonds in the structure ͑Fig. 3͒, we propose the transfer
of the sodium charge to the Sb-Sb bonds. Further details
will be discussed in a forthcoming publication about the
chemical bonding and electronic structure in the skutteru-
dites MFe4Sb12 ͑M=alkali, alkaline-earth, or rare-earth
metal͒.44 Following the ELF representation, the whole
structure of NaFe4Sb12 has to be considered as a three-
dimensional covalently bonded polyanionic framework of
iron and antimony atoms with sodium cations embedded
into the cavities. This scenario is in good agreement with
the rigidity of the structure found from the experimental
thermal expansion and compressibility.
FIG. 3. (Color online) Electron localization function ␩ for
NaFe4Sb12. (a) Crystal structure of NaFe4Sb12 with shortest inter-
atomic distances Fe-Sb and Sb-Sb. Isosurfaces of ELF illustrate
the covalent interaction between Fe and Sb ͑␩=0.53͒ and between
antimony atoms ͑␩=0.56͒. The isosurface with ͑␩=0.72͒ shows the
structuring of the third shell for the iron atoms; see text. (b) Elec-
tron counts for relevant bonds in the NaFe4Sb12 structure.
The significantly larger bulk modulus of IrSb3 can be ra-
tionalized considering the larger number of electrons avail-
0
able for bonding in ͓Ir4Sb12͔ in comparison with
0.98−
͓Fe4Sb12͔
.
The influence of this bonding mechanism on the magne-
tism and transport properties9,45 can be understood from the
results of the band structure calculations. The density of
states and band structure data for NaFe4Sb12 calculated by
the LMTO and FPLO procedures are in good agreement.
Figure 4 shows the total as well as the partial Fe and Sb
DOS from the spin-polarized calculation (FPLO) for
NaFe4Sb12. Due to the high DOS value of 42 states
eV−1 f.u.−1 for the paramagnetic solution (see Fig. 5 in Ref.
9), spin splitting of the mainly Fe 3d-related states leads to a
considerable reduction of the total energy ͑0.236 eV/f.u.͒,
resulting in a ferromagnetic ground state with a magnetic
Each attractor has a so-called basin defined by zero-flux
surfaces in the gradient field of ELF.41 The lowest ELF val-
ues on the border between two basins are called interconnect
points. The lower the ELF value at the interconnecting point,
the better the basins are separated; consequently, there exists
a larger charge separation. The basin of the sodium inner
shell interconnects with the framework basin only at a very
low value of ␩Ͻ0.1. Both facts—the absence of bonding
attractors in the vicinity of sodium atoms and the clear
charge separation—strongly suggest a charge transfer from
sodium to the Fe-Sb framework. Another relevant topologi-
cal feature of ELF in NaFe4Sb12 is the structuring of the
inner shell of the iron atoms [see isosurface with ␩=0.72 in
Fig. 3(b)]. According to Ref. 41 this suggests a participation
of the inner-shell electrons of iron in the interactions in the
valence region between the atoms.
moment of 2.97␮ per cell. The most striking feature on the
B
DOS plot is the almost negligible contribution of the major-
ity channel ͑DOS ͒ at the Fermi level. It amounts to
↓
0.1 eV−1 f.u.−1 only, compared to 21.1 eV−1 f.u.−1 for the mi-
nority states ͑DOS ͒. This results in a spin polarization of
↑
͑DOS −DOS ͒/͑DOS +DOS ͒=0.99, and thus, an almost
↑
↓
↑
↓
perfect half-metallic behavior of the compound.
Integration of the total electron density in the ELF basins
for the Sb-Sb attractors gives electron counts of 1.74 and
1.79 for d1͑Sb-Sb͒ and d2͑Sb-Sb͒, respectively. For the Fe-
The results for the isovalent KFe4Sb12 compound are
nearly identical. From the very similar features in the energy
214418-5

LEITHE-JASPER et al.
PHYSICAL REVIEW B 70, 214418 (2004)
FIG. 4. (Color online) Total, Fe 3d, and Sb 5p
derived density of states, respectively, for
NaFe4Sb12 for the ferromagnetic state. The Fermi
level is at zero energy.
region between −2 eV and 2 eV in the partial Fe 3d and Sb
5p DOS we can conclude a strong hybridization of these
states (i.e., bonding) in agreement with the ELF results. This
is also confirmed by “fat band analysis” of the Fe 3d and Sb
5p states (not shown). The Na (K) contribution to the occu-
pied states is small. The Na 3s states overlap with Sb 5p
states in the entire valence region (between −5 eV and EF).
The corresponding spin-polarized band structure for the
valence band region of NaFe4Sb12 is presented in Fig. 5. It
shows that only one majority (↓) band crosses the Fermi
level, whereas five minority bands (↑) contribute to the
Fermi surface. The majority band (↓) at the Fermi level is
dominated by Sb 5p states, whereas the minority (↑) bands
are mainly due to Fe 3d. The high DOS for the minority
channel results from the rather flat dispersion of the minority
bands in parts of the Brillouin zone (see Fig. 5 around the H
point). For a comparative study of the influence of different
filler cations on the electronic structure of skutterudites and
the importance of spin fluctuations we refer to Ref. 44.
C. Magnetic properties
The magnetization M͑T͒ of SPS-compacted samples of
NaFe4Sb12 and KFe4Sb12 in different external magnetic fields
Hext is displayed in Fig. 6. The new alkali-metal compounds
order ferromagnetically at TCϷ85 K. The magnetization per
Fe atom for both the Na and the K compound reaches about
0.52␮ at 1.8 K in the highest external field of the SQUID
B
magnetometer ͑70 kOe͒. The gross features for the ZFC and
FC curves in lower external fields are the same for both
compounds: the ZFC and FC curves are indistinguishable for
fields of 10 kOe and higher; thus, domain effects do not play
an important role and the isotherms are reversible. However,
the magnetic moment at 10 kOe is about 25%–30% less than
in 70 kOe. For Hext=1 kOe and lower fields a clear ZFC-FC
splitting is observed, typical for ferromagnetic domain ef-
fects. An interesting feature of the FC curve for Hext
=10 kOe of KFe4Sb12 is that M͑T͒ decreases with decreasing
temperature below 20 K. This effects was reproduced on a
different SPS-treated bulk sample and on purified KFe4Sb12
powder. This unusual behavior exists only for Hext
Ϸ10 kOe where M͑H͒ (see below) becomes reversible and
is probably connected to domain effects.
Isothermal magnetization loops provide further informa-
tion on the ferromagnetic state. For the current sample of
NaFe4Sb12 (SPS, Fig. 7) the remanent moment Mr per Fe
atom at 1.8 K is 0.25␮B which is slightly smaller than for the
previously published sample9 ͑0.28␮ ͒. M͑H͒ at 1.8 K in-
B
creases smoothly with field and reaches 0.60␮ in Hext
B
=140 kOe (sample from Ref. 9). The low remanent moment
and the continuous increase with Hext are due to strong spin
fluctuations (see below). Almost identical M͑H͒ curves are
found for as-prepared powder, purified powder, and SPS-
FIG. 5. (Color online) Band structure of NaFe4Sb12 for the fer-
romagnetic state; the Fermi level is at zero energy; the minority (↑,
solid lines) and majority bands (↓, dashed lines).
214418-6

WEAK ITINERANT FERROMAGNETISM AND…
PHYSICAL REVIEW B 70, 214418 (2004)
FIG. 8. (Color online) Magnetization per Fe atom versus exter-
nal magnetic field for SPS-treated KFe4Sb12. Isotherms were regis-
tered for nine different temperatures out of which three are shown.
(0.74␮B per Fe atom9). The hysteresis curves close for exter-
nal fields around 10 kOe (Fig. 8). For powder samples the
magnetization loop is more rounded off (not shown), the
coercive field is only Ϸ0.6 kOe (while HcϷ1.2 kOe for SPS
samples), and the remanent moment is a little smaller due to
the different ferromagnetic domain structure. With increasing
temperature the magnetization loops become regularly
smaller and narrower as demonstrated for SPS treated
KFe4Sb12 in Fig. 8.
Data of the paramagnetic susceptibility of Fe-containing
skutterudite materials11,46 where the filler cation does not
have a magnetic moment are scarce. The data analysis is
often hampered by the contribution of a ferromagnetic impu-
rity. The inverse magnetic susceptibility H/M (Fig. 9) in the
paramagnetic range can thus be significantly field dependent.
Assuming a saturation of the magnetization of the ferromag-
netic impurity in fields well above 10 kOe the susceptibility
M/H of the skutterudite can be extrapolated from data taken
FIG. 6. (Color online) Magnetization per Fe atom versus tem-
perature for different external magnetic fields Hext for SPS-treated
NaFe4Sb12 and KFe4Sb12. Generally, the lower-lying curves for a
field are the ZFC runs. For Hext=1 kOe, ZFC runs (᭝), FC runs
(᭞).
treated NaFe4Sb12 and KFe4Sb12 samples. The observed
magnetic moment for Hext=140 kOe (0.60␮B, and 0.65␮
B
when extrapolating M to 1/H→0) is only little less than the
moment obtained from fixed spin moment calculations
FIG. 7. (Color online) Isothermal magnetization ͑T=1.8 K͒ per
Fe atom versus external magnetic field for SPS-treated NaFe4Sb12
(sample from Ref. 9) and non-SPS CaFe4Sb12 powder. Data below
70 kOe (SQUID magnetometer) and up to 140 kOe (extraction
method) were combined.
FIG. 9. (Color online) Inverse magnetic susceptibilities H/M͑T͒
for different external magnetic fields and extrapolated values ͑H
→ϱ͒ for an SPS-treated sample and a purified powder sample of
KFe4Sb12. The line represents the Curie-Weiss fit for the SPS bulk
sample listed in Table II.
214418-7

LEITHE-JASPER et al.
PHYSICAL REVIEW B 70, 214418 (2004)
TABLE II. Results of Curie-Weiss fits on M/H͑T͒ data for filled skutterudite samples: external field [ϱ=extrapolated by the Honda-
Owen method (Ref. 47)], paramagnetic effective moment per Fe atom ␮eff (typical e.s.d. 0.05␮B), and Weiss temperature ⌰ from the fit. The
mass content of metallic iron impurity is derived from the difference of magnetization taken in fields of 35 kOe and 70 kOe.
Hext
Tmin/max
␮
⌰
Fe content
eff
Sample
[kOe]
[K]
͓␮ ͔
B
[K]
͓␮g/g͔
NaFe4Sb12 SPS bulka
NaFe4Sb12 SPS bulk
NaFe4Sb12 powderb,c
KFe4Sb12 SPS bulk
KFe4Sb12 powderc
ϱ
ϱ
150/400
150/350
150/400
150/400
150/400
1.76
1.68
1.60
1.66
1.67
+77.5͑3͒
+76.4͑4͒
+87.9͑1͒
+81.7͑3͒
+86.7͑2͒
Ϸ600
Ϸ1000
Ͻ5
70
ϱ
Ϸ500
Ͻ5
70
CaFe4Sb12 SPS bulkb
CaFe4Sb12 powderc
BaFe4Sb12 SPS bulk
BaFe4Sb12 powderc
ϱ
70
ϱ
150/390
150/400
150/380
130/380
1.51
1.51
1.61
1.57
+45.7͑5͒
+49.3͑7͒
+9.9͑4͒
50
10
Ϸ90
25–30
ϱ
+15.0͑9͒
aSample from Ref. 9 with lower density.
bSample contained ca. 5 vol % Sb metal.
cSample washed in HCl in order to remove the impurity of metallic Fe.
in 35 kOe and 70 kOe external fields (Honda-Owen
method47).
magnetic effective moment with field which may be due to a
small dampening of spin fluctuations with increasing exter-
nal field. These subtle effects, however, require further inves-
tigations.
In order to remove the impurity, powder samples were
washed in HCl. The field dependence of ␹͑T͒ of these puri-
fied materials is very small; thus, the ferromagnetic impurity
was almost completely removed. Figure 9 demonstrates that
the extrapolation method allows to extract the intrinsic sus-
ceptibility even for “impure” SPS material. Calculating the
impurity content from the saturation magnetization of Fe
͑222 emu/g͒ a mass fraction of 5–30 ␮g/g iron is found in
the cleaned powders (see Table II). Unfortunately, by sinter-
ing, the impurity content increases again. The Fe metal con-
tent in SPS samples is estimated to be between 50 and
Ϸ1000 ␮g/g.
Interestingly, for the purified KFe4Sb12 material, ␹͑T
Ͼ120 K͒ is minimal for H=20 kOe and increases both for
larger (35 kOe, 70 kOe; see Fig. 10, right panel) and smaller
fields (10 kOe, influence of tiny residual iron impurities).
This effect does not exist for the purified CaFe4Sb12 sample
(Fig. 10, left panel), which displays only the influence of
residual Fe metal impurities on ␹͑T͒. The increase of ␹͑T͒
above 20 kOe for KFe4Sb12 signals an increase of the para-
From the magnetization data for Na and KFe4Sb12 the
following picture evolves. Both alkali-metal skutterudites are
weak itinerant electron ferromagnets with a small spontane-
ous magnetization which increases strongly with the applied
field. Remarkably, the magnetic hysteresis behavior of
Na/KFe4Sb12 is significantly harder than that of the half-
metallic ferromagnets Co1−xFexS2 with pyrite structure.48
In the alkaline–earth-metal compounds CaFe4Sb12 and
BaFe4Sb12 no magnetic phase transitions are observed down
to 2 K (Figs. 11 and 12). SPS-treated material again shows
the influence of ferromagnetic impurities in the paramagnetic
susceptibility, but the iron contents are lower in the Ca and
Ba compounds than in NaFe4Sb12 and KFe4Sb12 samples.
However, even the purified powder sample of CaFe4Sb12 dis-
FIG. 10. (Color online) Field dependence of the susceptibility
␹=M/H of purified powder samples of CaFe4Sb12 (left panel) and
KFe4Sb12 (right panel). The differences ⌬␹ to the respective Curie-
Weiss fit of the susceptibility data taken in Hext=70 kOe is shown
(see text).
FIG. 11. (Color online) Magnetization per Fe atom versus tem-
perature for different external magnetic fields for purified powder of
CaFe4Sb12.
214418-8

WEAK ITINERANT FERROMAGNETISM AND…
PHYSICAL REVIEW B 70, 214418 (2004)
or KFe4Sb12. The apparent difference is the paramagnetic
Weiss temperature: while all ⌰ are positive (ferromagnetic)
and almost identical to the Curie temperature TCϷ85 K for
the alkali-metal compounds, the ⌰ for the Ba compound is
much smaller. For CaFe4Sb12 ⌰ is still remarkably large
͑⌰Ϸ50 K͒ whereas no sign of long-range order is detected.
The differences of our findings with the parameters ␮eff,
⌰ extracted in Ref. 11 for CaFe4Sb12 ͓1.85͑10͒␮B,
+3͑1͒ K͔ and BaFe4Sb12 ͓2.0͑1͒␮B,−36͑1͒ K͔ from the sus-
ceptibility measurements in Hext=30 kOe are probably due
to the presence of ferromagnetic impurities in the samples
which were not accounted for in the data evaluation. Due to
the different preparation route, the amount of ferromagnetic
iron impurities is often negligible in rare-earth-filled skut-
terudites.
In fact, LaFe4Sb12 has a significantly smaller ␮eff/Fe atom
FIG. 12. (Color online) Magnetization per Fe atom versus tem-
perature for different external magnetic fields for purified powder of
BaFe4Sb12.
than the alkali- and alkaline-earth-filled skutterudites [1.1␮
B
(Ref. 50), 1.12␮B (Ref. 46)], which fits in the observed trend
of a smaller effective moment with increasing charge of the
cation. As already pointed out,46 a simple ionic model is
inadequate since Fe-containing skutterudites are itinerant
magnetic systems. Electrical resistivity measurements9,45
confirm that all four compounds are “bad metals” with room-
temperature resistivities of 220–530 ␮⍀ cm.51 As our calcu-
lations prove,9,44 naturally, the major part of the moment
stems from the d-band polarization of the iron atoms and Sb
atoms display a small counter-polarization.
plays a change of slope at TϷ70 K and a plateau in ␹͑T͒
around 40 K. In BaFe4Sb12 (Fig. 12) similar features also
signal magnetic ordering phenomena. Upturns of the FC sus-
ceptibility for low external fields and much smaller ZFC sig-
nals may indicate precursor effects of ferromagnetic polar-
ization below ca. 20 K in both compounds. The temperature
of these features is approximately that of the Weiss tempera-
tures ⌰; thus, the presence of a nearly ferromagnetic metallic
state with strong spin fluctuations is indicated.
Our observation of Curie-Weiss laws with similar values
Summarizing, all our results indicate that a bulk ferro-
magnetic state exists only for the alkali-metal skutterudite
compounds. Magnetization measurements in high magnetic
fields up to 140 kOe on a CaFe4Sb12 powder sample (Fig. 7)
show no sign of a possible itinerant electron-metamagnetic
transition (see, e.g., Ref. 49) to a ferromagnetic state.
The high-field susceptibilities for purified samples are dis-
played in Fig. 13 in the H/M representation. The values
resulting from fits of a Curie-Weiss law (least-squares fits to
M/H) to these data in the paramagnetic range are given in
of ␮ and different ⌰ is consistent with Moriya’s self-
eff
consistent renormalization (SCR) theory52 of weak itinerant
ferromagnets. The behavior in the paramagnetic range is
governed by spin fluctuations. The positive ⌰ values of both
the alkali and alkaline-earth skutterudites are determined by
the Stoner factor. As already discussed in our previous Letter,
spin fluctuations play a crucial role in the formation of fer-
romagnetism in alkali and alkaline-earth metal iron antimony
skutterudites.9 In the former compounds of Na and K the
energy gain in the ferromagnetic state overcomes the imped-
ing fluctuations while the smaller energy gain for alkaline-
earth metal (Ca, Ba) skutterudites is insufficient for a static
polarization of the d bands even at T=2 K. Presumably, the
ferromagnetism depends on the subtle balance of dynamic
and quantum-critical spin fluctuations,44 as observed recently
for other itinerant ferromagnets (see, e.g., Ref. 53). In fact,
our recent investigations by nuclear magnetic resonance
methods on 23Na and 139La nuclei suggest a changeover from
weak itinerant ferromagnetism in NaFe4Sb12 to itinernant
nearly antiferromagnetism in LaFe4Sb12,50 according to the
terminology of Moriya.52
Table II. The effective magnetic moments ␮ per Fe atom
eff
are similar for alkali and alkaline-earth skutterudites, how-
ever, Ca and BaFe4Sb12 show slightly lower values than Na
D. Mössbauer spectroscopy
The presence of the Mössbauer-active atoms 57Fe and
121Sb in the compounds under study enables us to explore
their local surrounding and nuclear hyperfine parameters.
The room-temperature 57Fe Mössbauer spectrum of
NaFe4Sb12 (Fig. 14) is a paramagnetic doublet with isomer
shift ␦͑Fe͒=0.258͑4͒ mm s−1, quadrupole splitting ⌬EQ͑Fe͒
=0.21͑1͒ mm s−1, and linewidth 0.256͑7͒ mm s−1. These val-
FIG. 13. (Color online) Inverse magnetic susceptibilities H/M
of purified powder samples of filled skutterudites.
214418-9

LEITHE-JASPER et al.
PHYSICAL REVIEW B 70, 214418 (2004)
FIG. 14. 57Fe Mössbauer spectra of NaFe4Sb12 recorded at
293 K and at 4.2 K K.
FIG. 15. 121Sb Mössbauer spectra of NaFe4Sb12 measured at
150 K and 4.2 K. Line positions of reference antimony compounds
are shown by arrows.
ues correspond formally to a ferriclike oxidation state of
iron, which is surrounded by six antimony atoms forming a
distorted octahedron. A comparison with literature data,54
where a correlation of ⌬EQ͑Fe͒ with the distortion of almost
square Sb4 units (Fig. 3) was sought for, shows a similar 57Fe
quadrupole splitting for Tl0.8Co3FeSb12. No lines of elemen-
tal iron were visible in the spectrum. At T=4.2 K a weak
hyperfine magnetic field Hhf͑Fe͒=16.4͑1͒ kOe is detected on
the iron nuclei (Fig. 14) in agreement with the bulk
ferromagnetism55 from magnetization data. The isomer shift
and quadrupole splitting extracted from the magnetically
split spectrum are ␦͑Fe͒=0.379͑2͒ mm s−1 and ⑀͑Fe͒
=0.09͑1͒ mm s−1, respectively.
0.41͑11͒ mm s−1 can be attributed to an Sb2O5 impurity.
Since the sample for the Mössbauer measurement was not
washed in HCl, Sb2O5 is most likely a product of hydrolysis
of intermediate sodium-antimonides in the material.
Upon cooling, the fit for the 121Sb Mössbauer spectrum of
NaFe4Sb12 reveals a small magnetic hyperfine splitting
Hhf͑Sb͒=10.4͑16͒ kOe, reflecting the ferromagnetic state.
This polarization of nonmagnetic antimony atoms is also a
characteristic of the itinerant magnetism in the skutterudites.
Applying an external field of 16 kOe the value of the
effective field Hhf on the iron nuclei increased to ca. 32 kOe.
This result is surprising, insofar as in the ferromagnetic state
a decrease of the effective field could be expected. Normally,
the Fermi contact term HF dominates in the expression de-
scribing the hyperfine field on the Mössbauer nucleus in a
metallic ferromagnet:
The antimony Mössbauer spectra recorded at 150 K and
4.2 K are shown in Fig. 15. The positions of Mössbauer lines
of Sb2O3, Sb2O5 and metallic Sb measured at 4.2 K are in-
dicated by arrows. These lines provide the isomer shift ref-
erence scale. Corresponding values of isomer shifts relative
to the source 121mSn ͑CaSnO3͒ are ␦͑Sb2O3͒
=−11.65͑2͒ mm s−1,
␦͑Sb͒=−10.84͑2͒ mm s−1,
and
Hhf = Hext + HF + HB + HD + HDM + HL + Hcond
,
␦͑Sb2O5͒=0.57͑2͒ mm s−1.
At 150 K a paramagnetic antimony spectrum with ␦͑Sb͒
=−10.03͑2͒ mm s−1 and ⌬EQ͑Sb͒=6.0͑6͒ mm s−1 (Fig. 15)
is observed. The spectrum confirms the existence of only one
crystallographic site of antimony. ⌬EQ͑Sb͒ is in the range of
shifts of the oxide Sb2O3 and of metallic antimony. This
large value of ⌬EQ͑Sb͒ indicates a local surrounding of low
symmetry where Sb is coordinated by two Sb and two Fe
atoms which form a distorted tetrahedron. A similar pro-
nounced magnitude of the quadrupole interaction was ob-
served in the binary skutterudite CoSb3.56 The presence of
this distortion agrees well with results of 121Sb nuclear quad-
rupole resonance (NQR) measurements.57 The weak broad-
ened line with relative intensity about 5% seen at T=4.2 K at
where Hext is the external magnetic field. The Fermi contact
term HF (negative) originates from the imbalance of spin
density of core s electron polarized by unpaired d electrons.
However, the LDA calculation (see above and Ref. 44)
shows that, in NaFe4Sb12, the polarization of the Fe 4s elec-
trons is positive (+0.006 68␮B; 3s polarization is
negligible)—i.e., has the same sign as the 3d electron polar-
ization. In order to understand this the remaining terms have
to be analyzed. Both the orbital term HB and the dipole term
HD, arising from the dipolar interaction of the nucleus with
the spin moment of the atom, are positive. The demagnetiz-
ing field HDM and the Lorentz field HL are both small. The
polarized conduction electron contribution through the Fermi
214418-10

WEAK ITINERANT FERROMAGNETISM AND…
PHYSICAL REVIEW B 70, 214418 (2004)
contact interaction Hcond is positive. There are no general
theoretical estimates for the magnitude of this contribution,
but it might be relatively large [Ϸ100 kOe (Ref. 58)]. How-
ever, in the case of half-metallic magnets, direct conduction
electron polarization may be important. One cannot exclude
that the sum of the dominant positive terms HB+Hcond will
prevail in this crude estimation of Hhf in half-metallic ferro-
magnets. As a result, in an external magnetic field the ob-
served hyperfine field could increase. Another reason leading
to the increase of the hyperfine field might be the damping of
spin fluctuations in external magnetic field (see above).
resistivity data the filled skutterudites of Na, K, Ca, and Ba
are bad metals.
The weak itinerant ferromagnetism of NaFe4Sb12 and
KFe4Sb12 is characterized by a rather high Curie temperature
and by small ordered magnetic moments which increase
strongly with the external field. The paramagnetic suscepti-
bilities of the alkaline-earth skutterudites as well as of the
alkali skutterudites both follow Curie-Weiss laws with al-
most identical effective magnetic moment. These observa-
tions demonstrate the presence of strong spin fluctuations in
the sense of the SCR theory of Moriya. From an experimen-
tal point of view, NaFe4Sb12 and KFe4Sb12 behave almost
identical. CaFe4Sb12 and BaFe4Sb12 are paramagnetic (nearly
ferromagnetic52) down to 2 K, in spite of sizable Weiss tem-
peratures from Curie-Weiss fits to the high-temperature sus-
ceptibility. In CaFe4Sb12 and BaFe4Sb12 the energy gain in
the ferromagnetic state is insufficient to overcome the spin
fluctuations. They can be addressed as nearly ferromagnetic
metals. By Mössbauer spectroscopy small hyperfine fields at
the iron and antimony sites were detected which are in agree-
ment with the weak d-band polarization. The hyperfine field
of iron is found to be parallel to the Fe d-shell polarization.
IV. CONCLUSIONS
Detailed chemical analysis and XRD crystal structure in-
vestigation show full occupancy of the sodium position in
the NaFe4Sb12 structure. No indication for off-center dis-
placement for Na atoms is found. Only a dynamical thermal
motion is present for Na. The chemical bonding is analyzed
within the concept of the electron localization function. This
analysis reveals a strong covalent character of the Fe-Sb and
0.98−
Sb-Sb interactions in the polyanion ͓Fe4Sb12͔
and an
ACKNOWLEDGMENTS
almost complete transfer of charge from sodium to the poly-
anion. The value of the bulk modulus ͓B0=85͑1͒ GPa͔ of
NaFe4Sb12 is lower than that of IrSb3, consistent with even
stronger covalent bonding in the latter skutterudite. The elec-
tronic structure is characterized by a ferromagnetic ground
state with a large spin polarization of 99% and, therefore,
almost perfect half-metallic behavior. Indeed, from electrical
We are indebted to G. Auffermann (powder neutron dif-
fraction), R. Cardoso-Gil (x-ray diffraction), N. Reinfried
(SPS treatments), and M. Hanfland (ESRF Grenoble, high-
pressure XRD). A.R. acknowledges the Zeit-Stiftung and
H.R. the Deutsche Forschungsgemeinschaft (Emmy-
Noether-Programm) for financial support.
Electronic address: jasper@cpfs.mpg.de
*
11 M. E. Danebrock, C. B. Evers, and W. Jeitschko, J. Phys. Chem.
Solids 57, 381 (1996).
†Permanent address: Moscow State University, Faculty of Physics,
Moscow, Russia.
12 M. Tokita, J. Soc. Powder Technol. Jpn. 30, 790 (1993).
13 G. K. White and M. L. Minges, Int. J. Thermophys. 18, 1269
(1997).
‡Permanent address: Kamerlingh Onnes Laboratory, Leiden Univer-
sity, Leiden, The Netherlands.
1 A. Breithaupt, Ann. Phys. (Leipzig) 9, 115 (1827).
2 W. Jeitschko and D. Braun, Acta Crystallogr., Sect. B: Struct.
Crystallogr. Cryst. Chem. 33, 3401 (1977).
14 L. G. Akselrud, P. Y. Zavalii, Y. Grin, V. K. Pecharsky, B. Baum-
gartner, and E. Wölfel, Mater. Sci. Forum 133-136, 335 (1993).
15 G. M. Sheldrik, computer code SHELXL-97, University of Göttin-
gen, Göttingen, 1997.
16 K. Lagarec and D. G. Rancourt, Nucl. Instrum. Methods Phys.
Res. B 129, 266 (1997).
17 H. Spiering, L. Deák, and L. Bottyán, Hyperfine Interact. 125,
197 (2000); ftp://iacgu7.chemie.uni-mainz.de/pub/effi
18 O. Jepsen, A. Burkhardt, and O. Andersen, computer code TB-
LMTO-ASA version 4.7, Max-Planck-Institut für Festkörperfors-
chung, Stuttgart, 1999.
19 U. Barth and L. Hedin, J. Phys. C 5, 1629 (1972).
20 O. K. Andersen, Phys. Rev. B 12, 3060 (1975).
21 A. Savin, A. D. Becke, J. Flad, R. Nesper, H. Preuss, and H. G.
von Schnering, Angew. Chem., Int. Ed. Engl. 30, 409 (1991).
22 A. Savin, O. Jepsen, J. Flad, O. K. Andersen, H. Preuss, and H.
G. von Schnering, Angew. Chem., Int. Ed. Engl. 31, 187 (1992).
23 M. Kohout, computer code BASIN, version 2.3, Max-Planck-
Institut für Chemische Physik fester Stoffe, Dresden, 2001.
24 R. F. W. Bader, Atoms in Molecules: A Quantum Theory (Oxford
3 C. Uher, Semicond. Semimetals 68, 139 (2001).
4 I. Shirotani, Y. Shimaya, K. Kihou, C. Sekine, N. Takeda, M.
Ishikawa, and T. Yagi, J. Phys.: Condens. Matter 15, S2201
(2003).
5 E. D. Bauer, N. A. Frederick, P.-C. Ho, V. S. Zapf, and M. B.
Maple, Phys. Rev. B 65, 100506(R) (2002).
6 N. A. Frederick, T. D. Do, P.-C. Ho, N. P. Butch, V. S. Zapf, and
M. B. Maple, Phys. Rev. B 69, 024523 (2004).
7 G. A. Slack and V. G. Tsoukala, J. Appl. Phys. 76, 1665 (1994).
8 B. C. Sales, in Handbook on the Physics and Chemistry of Rare
Earths, edited by K. A. Gschneidner, Jr., J.-C. G. Bünzli, and V.
K. Pecharsky (Elsevier, Amsterdam, 2003), Vol. 33, Chap. 211,
pp. 1–34.
9 A. Leithe-Jasper, W. Schnelle, H. Rosner, N. Senthilkumaran, A.
Rabis, M. Baenitz, A. Gippius, E. Morozova, J. A. Mydosh, and
Y. Grin, Phys. Rev. Lett. 91, 037208 (2003).
10 J. M. D. Coey and S. Sanvito, J. Phys. D 37, 988 (2004).
214418-11

LEITHE-JASPER et al.
PHYSICAL REVIEW B 70, 214418 (2004)
University Press, Oxford, 1999).
43 M. Kohout and A. Savin, Int. J. Quantum Chem. 60, 875 (1996).
44 H. Rosner et al. (unpublished).
25 K. Koepernik and H. Eschrig, Phys. Rev. B 59, 1743 (1999).
26 J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13 244 (1992).
27 H. Eschrig, Optimized LCAO Method and the Electronic Struc-
ture of Extended Systems (Springer, Berlin, 1989).
28 C. B. H. Evers, L. Boonk, and W. Jeitschko, Z. Anorg. Allg.
Chem. 620, 1028 (1994).
45 W. Schnelle et al. (unpublished).
46 D. Ravot, U. Lafont, L. Chapon, J. Tedenac, and A. Mauger, J.
Alloys Compd. 323-324, 389 (2001).
47 K. Honda, Ann. Phys. (Leipzig) 32, 1027 (1910).
48 K. Ramesha, R. Seshadri, C. Ederer, T. He, and M. A. Subrama-
nian, Phys. Rev. B 70, 214409 (2004).
29 N. T. Stetson, S. M. Kauzlarich, and H. Hope, J. Solid State
Chem. 91, 140 (1991).
49 N. V. Mushnikov and T. Goto, J. Phys.: Condens. Matter 11, 8095
(1999).
30 C. B. H. Evers, W. Jeitschko, L. Boonk, D. J. Braun, T. Ebel, and
U. Scholz, J. Alloys Compd. 224, 184 (1995).
50 A. A. Gippius et al. (unpublished).
31 B. C. Chakoumakos, B. C. Sales, D. Mandrus, and V. Keppens,
Acta Crystallogr., Sect. B: Struct. Sci. 55, 341 (1999).
32 M. D. Hornbostel, E. J. Hyer, J. H. Edvalson, and D. C. Johnson,
Inorg. Chem. 36, 4270 (1997).
51 The electrical resistivity of polycrystalline samples strongly de-
pends on their porosity which can be effectively reduced by SPS
treatment (see, e.g., Ref. 59). Previous samples had resistivities
of order 1500 ␮⍀ cm at 300 K.
33 D. Cao, F. Bridges, S. Bushart, E. D. Bauer, and M. B. Maple,
Phys. Rev. B 67, 180511(R) (2003).
52 T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism
(Springer-Verlag, Berlin, 1985).
34 The difference electron density was studied based on single-
crystal XRD data ͑T=295 K͒. For that purpose a difference Fou-
rier synthesis based on ͉Fo͉−͉Fc͉ was calculated with the Na
atom removed from the refined model.
53 A. Aguayo, I. I. Mazin, and D. J. Singh, Phys. Rev. Lett. 92,
147201 (2004).
54 G. J. Long, B. Mathieu, B. C. Sales, R. P. Hermann, and F. Grand-
jean, J. Appl. Phys. 92, 7236 (2002).
35 J. L. Feldman, D. J. Singh, I. I. Mazin, D. Mandrus, and B. C.
Sales, Phys. Rev. B 61, R9209 (2000).
55 Mössbauer spectroscopy is insensitive to spin fluctuations on a
time scale of 10−8 s or faster.
36 J. L. Feldman, D. J. Singh, C. Kendziora, D. Mandrus, and B. C.
Sales, Phys. Rev. B 68, 094301 (2003).
56 I. Lefebvre-Devos, M. Lassalle, X. Wallart, J. Olivier-Fourcade,
L. Monconduit, and J. C. Jumas, Phys. Rev. B 63, 125110
(2001).
37 T. Caillat, A. Borshchevsky, and J. Fleurial, J. Appl. Phys. 80,
4442 (1996).
38 F. D. Murnaghan, Proc. Natl. Acad. Sci. U.S.A. 30, 244 (1944).
39 U. Schwarz, M. Schmidt, R. Gumeniuk, W. Schnelle, M. Hanf-
land, K. Klementiev, and Y. Grin, Z. Anorg. Allg. Chem. 630,
122 (2004).
57 A. Rabis, A. Leithe-Jasper, A. A. Gippius, E. Morozova, M.
Baenitz, W. Schnelle, N. Senthilkumaran, J. A. Mydosh, F. Steg-
lich, and Y. Grin, J. Magn. Magn. Mater. 272-276, 830 (2004).
The hyperfine field values for the Na site have to be multiplied
by 0.1 (in print); Phys. Rev. Lett. 93, 089904(E) (2004).
58 Chemical Applications of Mössbauer Spectroscopy, edited by V. I.
Goldanskii (Academic Press, New York, 1968).
59 L. Yang, J. S. Wu, and L. T. Zhang, J. Alloys Compd. 364, 83
(2003).
40 T. S. Snider, J. V. Badding, S. B. Schujman, and G. A. Slack,
Chem. Mater. 12, 697 (2000).
41 M. Kohout, F. R. Wagner, and Y. Grin, Theor. Chem. Acc. 108,
150 (2002).
42 ELF-hompage http://www.cpfs.mpg.de/ELF/index.html
214418-12